This assumption is standard [1]}, [2]} and also implies \(\mathbb {E}\left[ \xi _i\left( t \right) \left| \mathcal {F}_{t-1} \right. \right] =0\) . Note that if \(\mathbb {E}[ \left| \xi _i\left( t \right) \right|^2\left| \mathcal {F}_{t-1} \right. ] \le \nu ^2\)  holds for \(i\in \mathcal {V}\)  and \(t \ge 0\) , combined with Assumption 1(d), then Assumption 2 holds with \(\hat{L}=L^2+\nu ^2\) .
